Life without answer keys?

Recently I've been exchanging emails with Alexander Givental, who has translated the famous Russian book Kiselev's Geometry into English.

He's raised some interesting points regarding answer keys. I will just quote him directly from his emails to me. The discussion concerns geometry problems (please see the earlier post for examples).

"What is actually accomplished by supplying any solution at all? Ideally a student should be able not only to find a solution himself, but also be able to check that his solution is correct. With the aid of a written colution, the exercise is rendered useless for both purposes. Furthermore, a beginning student who finds a more complex solution (or may be even the same solution but eplained differently) may decide - incorrectly! - that his solution was wrong.

So, comparing your solution with your classmate's, teacher's, or parent's one makes sense, but with the one written in a silent book - very little. That's why, I think, no one bothered to write solutions for "Kiselev".

There is one general problem with solution books: there are many ways to describe the same solution to a problem, and there may be many solutions to the same problem; so it requires just as much expertise from a reader to figure out if his own solution is correct by reading somebody else's solution as it would without it. That is why collections of problems *with* solutions (which do exist in geometry), typically deal with higher range of difficulty than Kiselev's problems, are written in a very concise style and intended for highly experienced readers. BTW, for more than a hundred years of systematic use of Kiselev's book in Russia, it didn't occur to anyone to publish a solution manual. This should tell you something.

Teacher's guides are intended to save a teacher, clueless about the subject he teaches, from the embarassment in front of the class. They don't make him less clueless for, if they did, then teacher's guides would be used in place of textbooks. With or without teacher's guides,
a clueless instructor - teacher or parent - is of little help to the student. Conclusion: teacher's guides are obstructions to learning - for the instructor, and therefore for the student."

I agree with some things here. Being able to check that your solution is right is indeed desirable. After all, real life situations won't come with an answer key either. You need to be pretty sure about your solution then.

But, I'm sure answer keys save many homeschooling families many frustration tears.

Maybe it would work if every parent had someone to turn to in moments of problems - support. It could be another person, or internet message board.

Maybe the existence of answer keys reflects the culture and the times: we want everything fast and easy. Even answers to math problems. No one wants to ponder on a math problem for more than ___ (fill in) minutes.

What do you think?

See also Challenging problems in math education

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